Find the length of a side of a square whose perimeter and
area have the same value.
help?
perimeter of a square is P=4s & the area of a square is A=s^2
so you know
s^2 = 4s
s^2 - 4s = 0
s(s-4) = 0
s = 0 or s=4
So the side is 4 units
check:
area = 4^2 = 16
per. = 4(4) = 16
Why did you stop? You were on the right track but forgot to make use of the most important piece of information given.
The perimeter of a square of side "s" is P=4s.
The area of the same square is A = s^2.
Find the length of a side of a square whose perimeter and area have the same value.
P = A = 4s = s^2
Can you take it from here?
To find the length of a side of a square whose perimeter and area have the same value, you can set up an equation using the formulas for perimeter and area of a square.
Let's denote the length of a side of the square as "s".
The formula for the perimeter of a square is P = 4s.
The formula for the area of a square is A = s^2.
Since we want the perimeter and area to have the same value, we can set up the equation:
4s = s^2
To solve this equation, we can rearrange it into a quadratic equation form by moving all terms to one side:
s^2 - 4s = 0
Now, we can factor out an "s" common to both terms:
s(s - 4) = 0
To find the values of "s", we set each factor equal to zero:
s = 0 or s - 4 = 0
The solution s = 0 is not meaningful in this context because it represents a square with no sides.
So, we are left with s - 4 = 0. Solving for "s":
s = 4
Therefore, the length of a side of the square is 4.